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Published January 1994 | Published
Journal Article Open

Stabilization of trajectories for systems with nonholonomic constraints


A new technique for stabilizing nonholonomic systems to trajectories is presented. It is well known that such systems cannot be stabilized to a point using smooth static-state feedback. In this note, we suggest the use of control laws for stabilizing a system about a trajectory, instead of a point. Given a nonlinear system and a desired (nominal) feasible trajectory, the note gives an explicit control law which will locally exponentially stabilize the system to the desired trajectory. The theory is applied to several examples, including a car-like robot.

Additional Information

© 1994 IEEE. Reprinted with permission. Manuscript received March 14, 1992; revised November 17, 1992. This work was supported in part by the NSF under grants ECS-87-1998 and IRI 90-14490, and by the CNRS. G. Walsh was supported in part by an NSF fellowship. Part of this research was done at the Laboratoire d'Automatique et d'Analyse des Systèmes in Toulouse, France during the summer of 1991. G. Walsh, D. Tilbury, and S. Sastry are grateful for the warm welcome they received there. The authors would like to thank Dr. Georges Giralt for many inspiring discussions and Andrew Teel for suggesting the two remarks after proposition one.

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